Question 1003289

given:

Two lines are perpendicular: means their slopes are same to each other
if the slope of line 1 is {{{m}}}, then the slope of line 2 is {{{m[p]=m}}}


Line 1 through ({{{-4}}},{{{ 1}}}) and ({{{-2}}},{{{ -3}}}): 
find the slope-intercept form of the equation or {{{y = mx + b}}} for this line using given points

*[invoke change_this_name10094 -4, 1, -2, -3]

so, your line 1 has equation {{{y=-2x-7}}}, and its slope is {{{m=-2}}}

and slope of the parallel line 2 is

{{{m[par]=-2}}}



so far the equation of line 2 is {{{y=-2x+b}}}

since given that Line 2 through ({{{2}}},{{{ 1}}}) =({{{x}}},{{{ y}}}), use this point to find {{{b}}} 

{{{1=-2*2+b}}}

{{{1=-4+b}}}

{{{b=1+4}}}

{{{b=5}}}

now we have the equation of line 2: {{{y=-2x+5}}} 


see them on a graph:

{{{drawing( 600, 600, -10, 10, -10, 10,
circle(2,1,.12),locate(2,1,p(2,1)),
circle(-4,1,.12),locate(-4,1,p(-4,1)),
circle(-2,-3,.12),locate(-2,-3,p(-2,-3)),
 graph( 600, 600, -10, 10, -10, 10, -2x-7, -2x+5)) }}}